Problema Solution
the height of a box is 8 in. the length is three inches more than the width. find the width if the volume is 144 cubic inches.
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let
l = the length of the box, l>0
w = the width of the box, w>0
h = 8 in the height of the box
V = 144 in^3 is the volume of the box
the length is three inches more than the width
l = 3 + w
the formula for the volume of a box is V = w*l*h
w*l*h = 144
plug l = 3 + w into the last equation
w*(3 + w)*8 = 144
by solving we find
w = 3 in
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the width of the box is 3 inches.